Cables are wound onto the drums required for transporting them and storing them--known as cable drums--in windings located adjacent one another such that the core is first completely covered with windings by a first layer, and then a second layer is wound in a corresponding manner over the first, and so forth, until the drum is full or the required length of cable has been wound. For each layer, the attempt is made to cause the cable to assume the shape of a cylindrical spiral as much as possible, with the individual windings being wound closely adjacent to one another. To this end, the cable being brought to the coil is conventionally not directed toward it during winding at the same angle of inclination as in the cylindrical spiral; instead, it is fed at an angle which deviates therefrom for the sake of providing a bias so that the winding being formed will be pressed as closely as possible against the adjacent winding already in place on the core. Depending upon the type and the characteristics of the goods to be wound, it is more or less difficult to attain the desired form of a cylindrical spiral for the second, and subsequent layers as well, once the first layer has been wound. As a rule, an operator is required for monitoring and correcting the winding process in order to attain the desired cylindrical spiral pattern. The reason for these difficulties is that at the beginning and end of the first layer between the first and last windings, respectively, and adjacent the end flanges, wedge-shaped gaps are formed, and the goods to be wound, for instance the cable, of the second layer tends to drop into this wedge to a greater or lesser extent. The error caused thereby is repeated in all the subsequent layers and is added to the irregularities occurring at the transition from one layer to the next. The more layers are wound, the greater the difficulty in forming an orderly transition from one layer to the next. A further problem is that layers disposed above one another are each in the form of one cylindrical spiral, and the windings of the various spirals cross over one another. When winding the goods onto a layer which has already been completed, it is frequently unavoidable for a portion of the winding now being formed to come loose from the winding immediately adjacent it and to drop into a part of the groove-like depression between two adjacent windings of the layer beneath it. The cylindrical spiral pattern is then completely destroyed, and the further windings take a zig-zagging course. The gap formed in a layer as a result may cause disruptions in the layer or layers above it. Such disruptions or irregularities in forming the layers impair the winding process, however, and may even cause damage to the goods being wound under some circumstances. Furthermore, an irregular coil is the result, which is undesirable.